Guess Number Higher or Lower II

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I'll tell you whether the number I picked is higher or lower.

However, when you guess a particular number x, and you guess wrong, you pay $x. You win the game when you guess the number I picked.

Example:

n = 10, I pick 8.

First round: You guess 5, I tell you that it's higher. You pay $5. Second round: You guess 7, I tell you that it's higher. You pay $7. Third round: You guess 9, I tell you that it's lower. You pay $9.

Game over. 8 is the number I picked.

You end up paying $5 + $7 + $9 = $21.

Given a particular n ≥ 1, find out how much money you need to have to guarantee a win.

Credits:Special thanks to @agave and @StefanPochmann for adding this problem and creating all test cases.

Solution

public class Solution {
     public int getMoneyAmount(int n) {
        if (n < 1) return 0;
        int[][] dp = new int[n + 1][n + 1];

        return get(dp, 1, n);
    }

    private int get(int[][] dp, int x, int y) {
        if (x >= y) return 0;
        if (dp[x][y] != 0) return dp[x][y];
        int max = Integer.MAX_VALUE;

        for (int z = x; z <= y; z++) {
            max = Math.min(Math.max(get(dp, x, z - 1) + z, get(dp, z + 1, y) + z), max);
        }

        dp[x][y] = max;
        return max;
    }
}